One suggestion:
Clean up a section of the bar near the tail end.
Turn a simple cylindrical bush, generously thick-walled, to be a tight push-fit on that area.
You might want to fit a grub-screw that will sink below the outer surface and touch one of the flats (use a shim pad to protect the surface), as the bush contacts the work-piece only on the edges.
Now support the work in the 4-jaw with the steady running on the bush – but ensure accurate centring in the chuck otherwise the outer end of the bar will try to move in a circle exaggerating the error, and cause a lot of problems.
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Another, based on a long-established trick for good-quality square bar, is to make two such bushes, both a tight push-fit. The first as above, the other split along its length to be gripped wrapped round the stock, in a 3-jaw chuck.
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Probably the ideal way for a task like that is to use a between-centres boring-bar if you have those and a T-slotted saddle on your lathe. You would still use a long drill for the pilot hole.